3,142 research outputs found
Lyubeznik numbers of monomial ideals
We study Bass numbers of local cohomology modules supported on squarefree
monomial ideals paying special attention to Lyubeznik numbers. We build a
dictionary between local cohomology modules and minimal free resolutions that
allow us to interpret Lyubeznik numbers as the obstruction to the acyclicity of
the linear strands of the Alexander dual ideals. The methods we develop also
help us to give a bound for the injective dimension of the local cohomology
modules in terms of the dimension of the small support.Comment: 28 page
Properties of Lyubeznik numbers under localization and polarization
We exhibit a global bound for the Lyubeznik numbers of a ring of prime
characteristic. In addition, we show that for a monomial ideal, the Lyubeznik
numbers of the quotient rings of its radical and its polarization are the same.
Furthermore, we present examples that show striking behavior of the Lyubeznik
numbers under localization. We also show related results for generalizations of
the Lyubeznik numbers.Comment: 17 page
Torsion functors with monomial support
The dependence of torsion functors on their supporting ideals is
investigated, especially in the case of monomial ideals of certain subrings of
polynomial algebras over not necessarily Noetherian rings. As an application it
is shown how flatness of quasicoherent sheaves on toric schemes is related to
graded local cohomology.Comment: updated reference
Distractions of Shakin rings
We study, by means of embeddings of Hilbert functions, a class of rings which
we call Shakin rings, i.e. quotients K[X_1,...,X_n]/a of a polynomial ring over
a field K by ideals a=L+P which are the sum of a piecewise lex-segment ideal L,
as defined by Shakin, and a pure powers ideal P. Our main results extend
Abedelfatah's recent work on the Eisenbud-Green-Harris conjecture, Shakin's
generalization of Macaulay and Bigatti-Hulett-Pardue theorems on Betti numbers
and, when char(K)=0, Mermin-Murai theorem on the Lex-Plus-Power inequality,
from monomial regular sequences to a larger class of ideals. We also prove an
extremality property of embeddings induced by distractions in terms of Hilbert
functions of local cohomology modules.Comment: 12 page
Tameness of Local cohomology of monomial ideals with respect to monomial prime ideals
In this paper we consider the local cohomology of monomial ideals with
respect to monomial prime ideals and show that all these local cohomology
modules are tame
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